Visualisation Interfaces

It is author’s belief that, in order to convey the full meaning of design optimisation data to the designer, an integration of visualisation techniques from Table 5 has to be carried out via a set of interactive visualisation interfaces. By coupling them synergistically, the designer can thus gain a comprehensive insight into the data under study. The effectiveness in evaluating alternative design solutions via the simultaneous analysis of specific design perspectives is consequently expected to be greater than the sum of the individual contributions of the integrated visualisation techniques.

The visual exploration of design optimisation data is conducted by means of three graphical interfaces. Each interface is focused on the representation of one of the visualisation perspectives relevant in optimisation problems: Euclidean space

representation, multidimensional data visualisation and specific design tools. An intuitive

and user-friendly implementation of such interfaces in a joint graphical user interface (GUI) is sought to further improve the visualisation of the complex information produced by design optimisation tools. The interactive selection of points on any interface triggers in real time an automatic update of the visualisation on the remaining interfaces. This provides a means to conduct in a more effective manner both the analysis of a single solution or the comparison of a number of design alternatives.

The three graphical interfaces are described below. Key concepts of the methodology are clarified and illustrated via specific screenshots of a visual exploration interface prototype developed by the author, the Integrated Exploration and Visualisation Interface (IEVI), displayed in Figure 29. Unless stated differently, all the figures of this chapter depict the results obtained from the optimisation of Problem (42) after tightening its constraint as follows:

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Figure 29. Default visualisation of the IEVI. The three most relevant data perspectives in optimisation problems are shown via the below-described interfaces:

ESI (top-right window), SDTI (top-left window) and MDVI (bottom window).

Euclidean Space Interface (ESI)

The primary objective of the ESI is the representation of the objective space in a simple and conventional way for up to three objectives, providing the value of the objective functions for each alternative design point computed throughout the optimisation procedure. The visualisation of higher-dimensional objective spaces can be achieved by means of the techniques described in the Multidimensional Data Visualisation Interface paragraph below.

Via the integration of Filtering, the sets of non-dominated, feasible and infeasible solutions can be graphically highlighted in the ESI. Further filtering criteria can be specified in the PCP, as shown later on.

In the ESI, it is also possible to plot any pair of design parameters of interest, as shown in Figure 30. This offers a double advantage. On the one hand, it is possible to investigate the effects of any Filtering operation also on the design and constraint spaces. On the

other hand, the selection of points to be analysed/compared on the two other interfaces can be conducted by means of a Filtering process performed in the ESI by specifying desirable ranges of values or interactively selecting the points of interest.

a) b)

Figure 30. Two magnified examples of the visualisation flexibility allowed in ESI. The feasible, non-feasible and non-dominated sets of points have been identified by means of Filtering and are represented through green points, grey points and yellow squares, respectively.

Valuable information can be rapidly obtained from the ESI, such as:

- The identification of the objectives minimum and maximum values for the sets of optimum or feasible points;

- The location of similar designs in the objective, design, and constraint spaces;

- The position of local Pareto regions, which correspond to different optimal

families of solutions;

- The density of optimal/feasible/infeasible design solutions in a specific area of the objective, design, and constraint spaces;

- The location in the objective, design, and constraint spaces of the solutions characterized by one or more specific active constraints;

- Optimisation formulation errors.

Multidimensional Data Visualisation Interface (MDVI)

In the MDVI, the PCP is the default multidimensional visualisation technique available to the designer due to its effectiveness in visualising high-dimensional data on a simple two- dimensional plot. Moreover, this method is particularly useful for identifying relationships among the design parameters and for checking constraint satisfaction and activation.

In the PCP all the variables of interest are represented on the graph together. However, since the axes are plotted side by side, the i-th dimension is linked at most to two other dimensions. In an n-dimensional problem, no information is visualised about the relationships among the i-th axis and the other (n-3) axes which are not by its sides. Therefore, it is evident there is a need for implementing the PCP in the MDVI so that it is possible to permute the axes. This allows finding out different views of the problem and other possible relationships among the design parameters. Such an approach, based on a manual permutation of the axes, can be extended by firstly identifying the minimal set of permutations required to avoid duplicate adjacencies among all the n! possible permutations [120].

Furthermore, the user is provided with the Filtering function, which enables him/her to analyse only those solutions within an established range of values for any design parameter of interest (Figure 31). Additionally, it is possible to select the sets of solutions to be displayed (separately or conjointly), including: feasible points, infeasible points and non-dominated points.

Figure 31. Visualisation of the points obtained through the manual Selective PCP

Ranges function for Filtering. In this case, the solutions within the ranges x1=[0,0.5]

and f=[-0.67334,- 0.4] are highlighted in the ESI through cyan x-markers.

As an alternative multidimensional visualisation technique, the SPM is well suited for discovering or checking correlations among the data, or comparing local relationships between couples of variables, constraints and objectives (Figure 32). In this case, the

Filtering function remains applicable, both by portraying particular sets of solutions

(feasible, infeasible or optimal) and by specifying desirable ranges of values for the parameters displayed in the bivariate graphs matrix. Additionally, a numerical analysis of data can be carried out on the SPM in a more straightforward way on the strength of the Cartesian coordinates system. For high-dimensional datasets, however, it is necessary to analyse separately different sets of dimensions, because of the dimensional limitation of the SPM.

Figure 32. Scatter plot matrix (SPM).

Specific Design Tools Interface (SDTI)

This interface is expressly designated to conduct specific data analysis tasks in particular design domains. Therefore, the definition of the interface architecture has to be adequately defined depending on the discipline-dependent technique(s) to be used, along with its interaction with the other interfaces. Furthermore, a trade-off between the benefits of its integration and the corresponding complexity added to the system needs to be made, considering, for instance, the satisfaction of the rules of diversity,

complementarity, decomposition and parsimony given by Baldonado et al. [10].

It has been previously outlined, as an example, the integration of carpet plots within an aircraft design optimisation framework, pointing out what are the advantages in assessing the satisfaction of performance requirements through such traditional aircraft sizing tool (Figure 33). An alternative data representation on the SDTI can be found in Guenov et al. [44], where multiple data views are shown conjointly for the visualisation of the Pareto set, in particular, geometry and constraint activation.

In general, the SDTI layout is dictated by the design context under study and the adopted visualisation strategies. For example, mention can be made of the employment of surrogate-model based visualization for design steering, as proposed by Yang et al. [123] for crashworthiness optimisation. The use of metamodel-driven visualisation for graphical design and optimisation is gaining considerable attention for overcoming many technological limitations associated with complex graphical design environments. Nevertheless, it is important to note that such a strategy represents a compromise between having a fast graphical design environment and the loss of accuracy due to the use of metamodels [68].

Figure 33. Visualisation of solutions for a conceptual aircraft design optimisation. The sets of feasible, non-feasible and non-dominated points are depicted in the ESI considering the same graphical notation of Figure 30. In the same interface, it is shown how any solution of interest can be interactively selected, updating in real time the two other interfaces. The designer is thus allowed to assess the satisfaction of performance and to conduct a numerical analysis of the selected point on the

In the case of generic optimisation problems that do not require the use of any discipline-

dependent technique, the SDTI can be used both to visualise the distribution histogram of

any design parameter, or as an extension of the ESI. An example of the first option is portrayed in Figure 29 and Figure 31 with the distribution of the objective f and x1;

whereas the latter option is considered in Figure 34.

Figure 34. An example of an alternative use of the SDTI for a generic optimisation problem, offering a three-dimensional plot of the filtered data depicted in Figure 31. It is also shown how the interactive selection of points can be facilitated by zooming-in on the filtered solutions, as displayed in the ESI.